sampling

Concept

Convolution with impulse

• in frequency domain
• shift

With impulse train

• repeated at each impulse

Sampling in time domain

• due to convolution theorem
• using the CTFT of impulse train

essentially, sampling - point-wise mult of signal with impulse train, is convolution with impulse train in freq domain -> explaining the periodic nature

Nyquist limit

• minimum sampling frequency needed to analyse a frequency
• the impulses need to be far apart enough to prevent overlaps of the freq distributions

due to the complex conjugate symmetry for real signals,

Low pass filtering

• remove high frequencies
• prevent aliasing at lower sampling rates

Extra